The most hard-line conservatives in the House are taking an unusually cautious approach to the Senate’s Obamacare replacement, promising to keep an open mind about whatever their colleagues across the Capitol send back.

It’s a change in strategy for the House Freedom Caucus.

When House leaders first released a health care bill in February, for instance, group members took to television talk shows to pan the plan as “Obamacare lite,” furious that it didn’t, in their eyes, do enough to unravel the 2010 health care law.

They also threatened to withhold their support until changes were made, and later won concessions.

For now, those hardball tactics have disappeared. As the Senate looks to pass its own health care legislation this week, those same House conservatives are taking a more measured approach — even as several conservatives in the Senate are currently balking at the bill.

“I would like it to be better, but if this is the best we can do across the whole conference and the whole Congress, I have to respect that,” said Rep. Scott Perry (R-Pa.), a Freedom Caucus member.

Freedom Caucus Chairman Mark Meadows (R-N.C.) said last week that he — and the majority of the group — would likely back the Senate measure if it includes a few changes offered by conservative ally Sen. Ted Cruz (R-Texas). And he’s signaled in recent weeks a willingness to bend on other Freedom Caucus priorities, including state waivers for Obamacare regulations that were essential to winning over the hard-liners’ support in the House just a few weeks ago.

As senators began negotiating, the Freedom Caucus refrained from taking formal positions on ideas floating around the upper chamber that many in their ranks would have once rushed to oppose. And Freedom Caucus vice chair Jim Jordan (R-Ohio) on Thursday said it’s unlikely that they’ll weigh in on the plan soon.

It’s a notable change in tone from the typically rigid negotiating tactics of the Freedom Caucus. And it’s all aimed squarely at allowing their Senate colleagues breathing room to conduct difficult negotiations.

“I’m optimistic that in the effort to find 51 votes in the Senate and 218 votes [in the House], that some of those compromises are being made,” Meadows told reporters Thursday, hours after the Senate released its initial health care plan.

Since the House passed its bill in May, the Freedom Caucus has kept a low profile, freeing Senate Majority Leader Mitch McConnell to find consensus without conservative House members blasting his every move.

In an interview late last month, Meadows even joked that his involvement would probably just tank the Senate process: “Leader McConnell doesn’t need Mark Meadows to tell how to get consensus in the Senate. And quite frankly, the more that Mark Meadows tries to help him get consensus, the more difficult it is for him to get consensus, and I’m very self-aware of that.”

It’s more than just simple courtesy. McConnell is working in a highly polarized Senate to cobble together 50 votes for a health care package. With no Democrats expected to support the measure, he can afford to lose only two of the chamber’s 52 Republicans.

Already, four conservative senators — Cruz, Mike Lee (R-Utah), Rand Paul (R-Ky.) and Ron Johnson (R-Wis.) — have said they can’t support the bill without amendments to dismantle more of Obamacare. A fifth senator, Dean Heller (R-Nev.), is pulling in the opposite direction, warning that the initial bill cuts too deeply into Medicaid and Obamacare’s protections for him to support it.

Meadows and the Freedom Caucus are still hoping to assert themselves before the final version of the bill is passed, but they’re doing it in uncharacteristically subtle ways.

The group’s leaders, including Meadows, Jordan and Raúl Labrador (R-Idaho), have kept in touch with conservative senators, especially Lee, as well as Johnson.

Meadows has also quietly been working with mainstream Senate Republicans to ward off changes that might erode conservative support — and to signal just how far his allies might be willing to go in accepting more moderate tweaks to the bill.

For example, he’s spoken to Sen. John Thune (R-S.D.) about Thune’s plan to increase tax credits for poorer individuals while cutting them on the wealthy. The Freedom Caucus has advocated against proposals for a refundable tax credit, but Meadows signaled in May that he’s open to Thune’s proposal.

Meadows also indicated several weeks ago that the Senate preference for a multiyear phase-out of Obamacare’s Medicaid expansion won’t necessarily be a deal-breaker, even though conservatives have grumbled that the House’s shorter window was already too generous. And Meadows even indicated that he could possibly back the Senate bill if it weakens a conservative-favored provision that the House included: allowing states to waive core Obamacare coverage standards.

“If the waivers come out, there will be a number of other options that are put in their place that could potentially be just as meaningful in driving down premiums,” he said.

There are also indications the Freedom Caucus’ muted approach could change. One conservative source said the group’s current stance isn’t necessarily indicative of its posture this week, as negotiations in the Senate continue.

Perhaps the most crucial bellwether for conservative support the fate of Cruz’s proposed amendments. The Texas firebrand has suggested allowing consumers to use their Obamacare tax credits to purchase insurance products that fall short of the health care law’s coverage standards. That “consumer choice” amendment, along with a few other conservative additions, would virtually guarantee a majority of the Freedom Caucus’ support, Meadows said Thursday.

Another flash point will come this week, when the Congressional Budget Office indicates the economic and coverage impact that the Senate bill is likely to have. CBO’s analysis suggested that the House bill would result in 23 million fewer people with health coverage in the next decade, a metric that spooked some moderate senators, who deemed the House measure a nonstarter.

Conservatives will be looking a different CBO number: how the Senate bill affects premium increases, the most important thing to them.

“If CBO says this will continue to bring down premiums, and it protects pro-life and Planned Parenthood defunding and all, I’m open to it,” Jordan said of the Senate proposal Thursday.

In the meantime, the drumbeat of news that insurers are pulling out of Obamacare’s individual market exchanges has provided fuel for Republicans to push ahead with their plans. And it appears to be making it easier for some conservatives to swallow compromises.

“Is the bill that the Senate kicked out or the House bill my dream bill? No, it is not,” Perry said. “However, the context is, what’s happening now is failing, and we have an obligation to do what we can to fix it as best we can.”